Any recommendations/tips/must do things while taking a short trip to Paris?

I fly out to visit the UK Aug 26th, arrive the 27th and will spend the bank holiday in Nottingham with my bf. We will be going to Paris for 2-3 days and even though I know there are quite a few must sees on my list of things to do I wanted to know if any of you wanted to throw some out there...? Maybe any books/travel guides? Places to eat? Cheap or free activities/sites to see/visit? Any great, moderately priced hotels? Has anybody done the Fat Tire Bike Tour? A friend of mine suggested I try that Oh and we'll also be visiting London for a few days I know there's a fair amount of people who live there any suggestions for that would be great as well. THANKS

Go up to Sacre Cour (may have spelt wrong) particularly at dusk.

Sainte-Chapelle, the Catacombs and Berthillon ice cream.

Go up to the top (restaurant) floor of the Institute du Monde Arabe:  http://www.paris-tourisme.com/museums/monde-arabe/index.html and you get a wonderful view of Paris (including the Eiffel Tower) for free. You can have an extremely expensive coffee but you don't have to buy anything if you don't want to.

The Rodin Museum.  http://www.musee-rodin.fr/welcome.htm

And eat crepes, lots and lots of crepes!

http://www.angelina-paris.fr/en/#/home/

Best hot chocolate ever!

Mint tea at the Mosquee de Paris.

Probably a bit morbid, but the tunnel where Princess Di was killed is very interesting. Maybe not search it out, but if you come across it, you'll know it.

I could only recommend the major sites (it's been about 12 years since I went to Paris).  Your trip is short, so unless you want to sacrifice at least one whole day in the Louvre, I might skip it all together and try it on another visit.

Go up to Sacre Cour (may have spelt wrong) particularly at dusk.

Close! It's the Sacré-Coeur. Just beware of some of the people who target tourists in that area. The steps leading up are narrow and men flank them, trying to attach a bracelet onto your wrist, forcing you to pay in order for them to let go. While I second the recommendation of going there (it's beautiful), I suggest keeping your hands in your pockets as you head up the steps. 

I quite liked going up the Arc du Triomphe for a good view - but make sure you're ready to climb lots and lots of steps! A walk through the Tuileries or Jardin du Luxembourg is always nice, too.

As for books, I can recommend a few as well as some apps. And yes, I am incredibly biased. 

http://traveldk.com/paris
DK Top 10 Paris app is available for iPhone and Android
Also available for iPad: http://itunes.apple.com/us/app/paris-dk-eyewitness/id403266639?mt=8
And then there are the lovely DK books. Top 10 Paris, for example: 


Rough Guides are also great travel books. They have an app as well (I can't recall if it's available on Android yet, though).

I've never heard any horror stories about the Sacre-Coeur and I've been 5 times.  Matter of fact, I'll be staying in Montmartre for the next seven days!

Advice: if you can get there for the first Sunday of the month hit all the museums and monuments you can, they're completely free entry.  If there is anything you absolutely HAVE to see and/or do, do it first otherwise you'll get sidetracked by everything else! 

One of the best books I've ever gotten, and STILL use each time I go is the Knopf Mapguides Paris, ISBN 0307263886 (yes, I have it at hand haha!)  The pages list interesting sites and flip out so that you get a rather detailed map of the area.  It's compact and easy to tote. 

As far as things to do, check out the Rue Cler, which is a pedestrian street near the Eiffel Tower.  It's one of those rare Parisian streets that has every type of shop you could imagine.  Also great is the Rue Mouffetard near the Mosque de Paris, which is also a fascinating piece of architecture.  Best of all, each of those are free. 

Have a great trip!

What kind of housing are you looking for?  If you are young and happy to stay in hostels, I LOVE this one:

http://www.mije.com/index_individuels_uk.asp

I've stayed there three or four times and had a great experience with it.  I believe they still have age limits though, so now I'm too old to go there   You can't beat their locations though and they are in these lovely old buildings.  The bedding is fairly standard hostel-fare, but the whole experience is great.

The Pere Lachaise cemetery is worth a visit, you can get lost in there for hours. Stunningly beautiful. http://www.perelachaisecemetery.com/

Here's a second for Sainte-Chapelle and Pere Lachaise.  They are not quite as big of tourist spots, but are so fun.  I've never seen stained glass before or since like Sainte-Chapelle.  It's really amazing.  Pere Lachaise is fun to just for the odd macabre factor.  Get a map before you go in so you can find all the famous graves.

Really though, even if you don't have set plans, Paris is one of those cities that is thoroughly enjoyable to just wander around.  Just walk up and down the river going off into roads and you'll find plenty to explore and be happy with. 

I can't really give restaurant recommendations as I've only eaten in a few since so much of my trip was filled with eating fun random things I found in odd street cafes and creperies.  There's no shortage of eateries around--and don't forget to find some good patisserie while you are there--you'll never want to set foot in Greggs (an abomination to the name of bakeries) again.

I can highly recommend the Shoah Memorial (it's a Holocaust museum). Not sure if that's your thing, but it is free to get in, and we thought it was excellent.  It is closed on Saturdays and kind of hard to find- it is not very well advertised and there weren't many signs for it.  More info here:

http://www.memorialdelashoah.org/b_content/getContentFromTopNavAction.do;jsessionid=95F053D084AB1A5E79BBEE9265B1EFAD?navId=94

Have a great trip- Paris is such a magical city!

Thank you ALL so much for all of your wonderful ideas/tips. I will be sure to fill in the boyfriend on these! I'm sure we may spend more time here then originally planned due to the riots and not sure if we'll be doing London